The present invention relates to methods and apparatuses for determining a magnetic field, a magnetic field vector or a value related thereto, more particularly for determining a static magnetic field signature associated with an object whereby the applied uniform magnetic field (such as associated with a test facility) and/or the earth""s background magnetic field are accounted for in such determination.
Laboratory measurement of the static magnetic fields surrounding large objects can be a difficult process. These experiments are typically conducted within the uniform volume of a large magnetic calibration facility whose coil system can apply fields in three orthogonal directions. In the past, such laboratory tests have included spacecraft, large-scale magnetic models of naval vessels, and full-scale ship equipment such as engines, electric motors, and generators. See the following papers, each of which is incorporated herein by reference: T. N. Roy, xe2x80x9cSpacecraft magnetic field modeling,xe2x80x9d IEEE Trans. Magn., vol. 13, pp 914-919, January 1977; A. V. Kildishev, S. A. Volokhov and J. D. Saltykov, xe2x80x9cMeasurement of the spacecraft main magnetic parameters,xe2x80x9d in Proc. 1997 IEEE Autotestcon Systems Readiness Technology Conf., pp 669-675, 1997; R. A. Wingo, J. J. Holmes and M. Lackey, xe2x80x9cTest of closed-loop degaussing algorithm on a minesweeper engine,xe2x80x9d in Proc. 1992 Amer. Soc. Naval Eng., May 1992. In naval applications, the field pattern around and under a ship is called its signature.
The purpose of laboratory experiments is usually to measure an object""s field at discrete locations around it, and then to mathematically predict the flux distribution or signature in all space. See F. M. Duthoit, L. Krahenbuhl and A. Nicolas, xe2x80x9cThe boundary integral equation method for the extrapolation of field measurement,xe2x80x9d IEEE Trans. Magn., vol. 21, pp 2439-2442, 1985, incorporated herein by reference.
In addition, onboard magnetic field compensation systems called xe2x80x9cdegaussingxe2x80x9d systems are adjusted (calibrated) to minimize the amplitude of the surrounding field. See the following papers, each of which is incorporated herein by reference: K. R. Davy, xe2x80x9cDegaussing with BEM and MFS,xe2x80x9d IEEE Trans. Magn., vol. 30, pp 3451-3454, September 1994; X. Xu and L. Zeng, xe2x80x9cDegaussing of cylinders magnetized in Earth""s magnetic fieldxe2x80x94a 2-D model of degaussing of submarine,xe2x80x9d J. Electromag. Waves Appl., vol. 12, pp1039-1051, 1998; F. Le Dorze, J. P. Bongiraud, J. L. Coulomb, P. Labie and X. Brunotte, xe2x80x9cModeling of degaussing coil effects in ships by the method of reduced scalar potential jump,xe2x80x9d IEEE Trans. Magn., vol. 34, pp 2477-2480, September 1998; M. Norgren and S. He, xe2x80x9cExact and explicit solution to a class of degaussing problems,xe2x80x9d IEEE Trans. Magn., vol. 36, pp 308-312, January 2000.
Minimization of a naval vessel""s static magnetic field signature is important in reducing its vulnerability to magnetically actuated mines. Also, spacecraft signature reduction is necessary to mitigate attitude control problems, and interference to onboard magnetic instruments and low-energy electron experiments. See aforementioned paper T. N. Roy, xe2x80x9cSpacecraft magnetic field modeling,xe2x80x9d IEEE Trans. Magn., vol. 13, pp 914-919, January 1977.
Large, triaxial, calibration coil facilities presently exist at several U.S. Naval facilities, including the Naval Surface Warfare Center detachment at Panama City, Fla. In addition, a new coil facility is under construction at the Center""s Carderock Division, West Bethesda, Md. that will accommodate test items up to 44 tons in weight. The new facility""s coil system will generate a uniform magnetic field within a cube 3 meters on a side, with a peak-to-peak spatial variation less than 0.05% of the field along the primary axis. An inducing field can be generated over the uniform volume with a dynamic range of xc2x150,000 nT, and can be held stable to within xc2x11 nT, according to D. Whelan of the Naval Surface Warfare Center, West Bethesda, Md. as stated in a private communication (e-mail) to joint inventor John J. Holmes on Jan. 18, 2000. However, laboratory testing of large magnetic objects can present special problems.
An important requirement for a magnetic testing facility is the ability to remove the applied uniform field (facility plus earth""s field) from the measurement of an item""s signature. Typically, the applied field is eliminated by physically removing the test object from the facility, then recording and storing the sensor readings while energizing each calibration coil, one at a time, with a known current. This xe2x80x9cbackgroundxe2x80x9d data can be scaled; based on real-time measured coil currents or other facility control sensors, and subtracted from all subsequent measurements of the test object. However, removing a test item from inside a coil system is not always viable, especially if the object is physically large, heavy, or has an irregular shape. In some cases, sensors and sections of the coils themselves must be moved to accommodate removal of the test item from the facility. Exact realignment of the sensors and coils is always difficult and time consuming, reducing accuracy and repeatability of the experiments.
A magnetic gradiometer measures the difference between two magnetometers separated by a short distance and mounted on a rigid and thermally stable bar that is usually made of titanium. Special care is taken in the design and construction of a gradiometer to insure that the gain and orientation of its two magnetometers do not change over time with environmental conditions. A commercial product which exemplifies this is Gradiometer Type GS2, manufactured by the ULTRA Electronics Magnetics Division, Fallow Park, Rugely Road, Hednesford, Cannock, Staffordshire, England WS12 5QZ.
In view of the foregoing, it is an object of the present invention to provide method and apparatus for measuring the magnetic signature of an entity so as to remove the influence of any external field (e.g., an applied magnetic field and/or the earth""s magnetic field) from such measurement.
It is a further object of the present invention to provide such method and apparatus for measuring the magnetic signature of an entity which is large or cumbersome or otherwise does not readily admit of portability or transportability relative to a magnetic test facility.
In accordance with many embodiments of the present invention, a method for determining at least one magnetic field signature of an entity comprises the steps of performing gradiometric measurements and processing the gradiometric measurements. The performing of the gradiometric measurements includes using plural gradiometers which are arranged so as to generally describe a closed three-dimensional geometric shape which surrounds the entity. The processing of the gradiometric measurements includes determining the multipole moments of the entity based on the gradiometric measurements, wherein the multipole moments correspond to the closed three-dimensional geometric shape. According to typical inventive embodiments, the closed three-dimensional geometric shape is a prolate spheroid which surrounds the entity, and the multipole moments are the prolate spheroidal multipole moments of the entity (i.e., the multipole moments pertaining to the same prolate spheroidal shape which is geometrically conceived to surround the entity as described by the arrangement of the gradiometers).
Further provided according to the present invention is a computer program product. The present invention""s computer program product comprises a computer useable medium having computer program logic recorded thereon for enabling a computer to determine at least one magnetic field signature of an entity. The computer program logic comprises means for enabling the computer to determine the prolate spheroidal multipole moments of the entity. The prolate spheroidal multipole moments (i.e., the multipole moments pertaining to the same prolate spheroidal shape which is geometrically conceived to surround the entity as described by the arrangement of the gradiometers) are based on gradiometric measurements performed using plural gradiometers which are arranged so as to generally describe a prolate spheroidal shape which surrounds the entity.
The present invention also provides apparatus for determining at least one magnetic field signature of an entity. The inventive apparatus comprises a plurality of gradiometers and a computer with which the gradiometers are electrically connected. The gradiometers are for performing gradiometric measurements whereby the gradiometers are arranged so as to generally describe a prolate spheroidal shape which surrounds the entity. The computer is for establishing relationships including the following: relationships between the gradiometric measurements and directional derivatives; relationships between the directional derivatives and the prolate spheroidal multipole moments (i.e., the multipole moments pertaining to the same prolate spheroidal shape which is geometrically conceived to surround the entity as described by the arrangement of the gradiometers); and, relationships between the prolate spheroidal multipole moments and the magnetic field(s) of the entity which exist(s) interior of the prolate spheroidal shape. According to some inventive embodiments, the computer is also used for optimizing the arranging of the gradiometers with respect to at least one parameter selected from the group consisting of the number of the gradiometers, the positions of the gradiometers, and the orientations of the gradiometers.
The term xe2x80x9cmagnetic fieldxe2x80x9d has been defined as a vector function field which is described by a magnetic induction. The term xe2x80x9cmagnetic fieldxe2x80x9d has also been defined as a field of magnetic force existing around a current-carrying conductor or magnetic body. The terms xe2x80x9cmagnetic signaturexe2x80x9d and xe2x80x9cmagnetic field signaturexe2x80x9d have been used in naval and other scientific and engineering contexts to mean a magnetic field pattern or configuration associated with an object. Technical parlance has seen the interchangeable use of the terms xe2x80x9cmagnetic field,xe2x80x9d xe2x80x9cmagnetic signaturexe2x80x9d and xe2x80x9cmagnetic field signaturexe2x80x9d so as to denote any of a variety of manifestations of magnetic field. As used in the instant disclosure, the terms xe2x80x9cmagnetic field,xe2x80x9d xe2x80x9cmagnetic field signaturexe2x80x9d and xe2x80x9cmagnetic signaturexe2x80x9d are interchangeable, each term broadly and synonymously referring to one or more magnetic fields or one or more components, portions or aspects thereof, or one or more magnetic field vectors or one or more components, portions or aspects thereof.
The present invention features inventively developed equations that relate magnetic gradiometric measurements over a closed surface to the prolate spheroidal multi-pole moments of an object. The present invention""s formulations can be used to remove the uniform inducing field of a magnetic calibration facility""s coil system, along with the earth""s background field, from the signature of a large test itemxe2x80x94without requiring that such large test item be moved.
In accordance with typical embodiments of the present invention, gradiometers are used for purposes of extrapolating and/or minimizing the static magnetic fields existing inside (within) a xe2x80x9csource-free volume.xe2x80x9d The extrapolation and/or minimization of the static magnetic fields is/are accomplished based on gradiometric measurements taken over the surface that inwardly bounds the source-free volume. The source-free volume is the entire three-dimensional space extending outwardly, into infinity in all directions, from the closed surface. The present invention""s methodology can be applied to other types of vector fields.
By practicing the present invention""s methodology described in this disclosure, the magnetic fields within a source-free volume can be extrapolated or computed based on gradiometric measurements over its bounding surface. The present invention""s technique allows the inducing magnetic field (the earth""s magnetic field and/or the testing facility""s applied field) to be removed from the measurements without physically separating the sensors from the magnetic object. The inventive method should increase the accuracy of extrapolating or canceling the magnetic field signature of large objects.
An inventive example is given herein that shows how the equations can be used to determine the optimum number, orientations and positions of gradiometers for accurate extrapolation of the object""s field signatures. In addition, generalized boundary conditions have been established herein that guarantee unique extrapolations of magnetic field, up to an additive constant, from a closed measurement surface instrumented only with gradiometers.
The present invention obviates the need for moving a test object for the purpose of removing the inducing coil""s applied uniform field from the object""s magnetic signature. A magnetic gradiometer can subtract the applied background field from an object""s signature. Since the applied flux at Carderock""s new coil facility is uniform over the small dimensions of the gradiometer (better than 10 nT/m), and since the worse case noise of a commercial gradiometer due to alignment error is better than 75 nT/m (See aforementioned Gradiometer Type GS2, ULTRA Electronics Magnetics Division, Fallow Park, Rugely Road, Hednesford, Cannock, Staffordshire, England WS12 5QZ), sufficient signal-to-noise can be obtained from close-in measurements of a test object""s field gradients.
Incorporated herein by reference is the following published paper, authored by one of the joint inventors, which discloses various aspects of the present invention: John J. Holmes, xe2x80x9cTheoretical development of laboratory techniques for magnetic measurement of large objects,xe2x80x9d IEEE Transactions on Magnetics, vol. 37, no. 5, September 2001, pages 3790-3797.
Other objects, advantages and features of this invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.